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Lehre der Trigonometrie anhand realistischer Aufgaben im Online-Unterricht
87-105Views:102The aim of our study was to explore the effects of the active use of realistic exercises in the field of trigonometry. We taught a group of 14 pupils, who were in grade 11. The most of them told us they did not plan mathematics-related studies in the future. We included realistic exercises into our teaching plan, which covered the fields of scalar product, as well as the sine and cosine theorems. Our teaching experiment was done within the framework of online teaching. Effects on the motivation, performance and results of the students were taken into consideration. We also attempted to examine the effects of online teaching on motivation and whether the use of realistic exercises is worthwhile in an online classroom environment. Performance of the students showed a tendency of improvement when they were dealing with the material through realistic exercises even despite the teaching happened online.
Subject Classification: 97C70, 97D40, 97G60
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Report of meeting Researches in Didactics of Mathematics and Computer Sciences: January 24-26, 2014 Eger, Hungary
117-134Views:8The meeting Researches in Didactics of Mathematics and Computer Sciences
was held in Eger, Hungary from the 24th to the 26th of January, 2014 at the
Eszterházy Károly College. It was organized by the PhD School of Mathematics and Computer Sciences of the University of Debrecen and the Eszterházy Károly College in Eger.
The 58 participants – including 43 lecturers and 18 PhD students – came from 7 countries, 15 cities and represented 22 institutions of higher education. -
Teaching of financial mathematics using Maple
289-301Views:49The paper deals with the application of computer algebra system Maple in teaching of financial mathematics. In the Czech Republic financial mathematics is included in the curricula of grammar and secondary school. Therefore, this subject is also taught at pedagogical faculties. Most concepts of financial mathematics are difficult to understand for students. In the paper we show the ways of facilitation understanding these concepts using tools of Maple. The main result is in preparing special maplets which enable interactive studying of the principles of such concepts. Each of these maplets deals with particular financial problem from real life, e.g. mortgage credit, consumer credit, credit card etc. -
The Project Method and investigation in school mathematics
241-255Views:27The Project Method (PM) is becoming more common in the teaching of mathematics. Most of the time, Project Method means solving open and relatively wide formulated problems for the application of particular mathematical topics and the solving of everyday life problems.
At present many experts in the theory of teaching mathematics advocate teaching activities as the characteristic for most mathematical work in the classroom. Thus, there is a question: whether it is possible or eventual desirable to use the PM for solving genuine mathematical problems. This paper deals with this question and discusses the connection between the PM and investigation of new mathematical knowledge for students. Our experience has shown that the PM in connection with investigations can be a useful and effective approach to teaching mathematics. -
Report of meeting Researches in Didactics of Mathematics and Computer Sciences: January 23-25, 2015 Novi Sad, Serbia
141-162Views:11The meeting Researches in Didactics of Mathematics and Computer Sciences was held in Novi Sad, Serbia from the 23th to the 25th of January, 2015 at the University of Novi Sad. It was organized by the PhD School of Mathematics and Computer Sciences of the University of Debrecen and the Department of Mathematics and Informatics of the University of Novi Sad.
The 70 participants – including 42 lecturers, and 18 PhD students – came from 9 countries, 28 cities and represented 40 intstitutions of higher education. -
Problem-solving in mathematics with the help of computers
405-422Views:27One of the most important tasks of the didactics of mathematics is the describing of the process of problem-solving activity and problem-solving thinking. The psychological theories concerning the problem-solving thinking leave the special demand of school subjects out of consideration, and search for connections of universal validity. In this article we attempt to connect an abstract theory of psychology concerning problem-solving thinking and a more practical conception of the problem-solving activity of mathematics, which is based on Polya's idea. In this way we can get a structure of problem-solving, which has scientific bases and at the same time it is useful in computer aided learning. Our result was developed and tested in Hungary so this is suitable especially for the Hungarian conditions of mathematics teaching. -
Fehleranalyse beim Lösen von offenen Aufgaben Ergebnisse einer empirischen Studie in der Grundschule
83-113Views:9Open problems play a key role in mathematics education, also in primary school. However, children in primary school work in many relations in a different way from learner in secondary school. Therefore, the (possibly) first confrontation with an open task could be problematical. Within the framework of an international paper and pencil test it was examined how far children of primary school notice the openness of a task and which mistakes they do during working on that task. In particularly are meant by openness different interpretations of the task, which all lead to a set of numbers with more than one element as a result. For evaluation, a common classification system was adapted by slightly modification of the original system. -
Development of high school students' geometric thinking with particular emphasis on mathematically talented students
93-110Views:13We carried out research using Zalman Usiskin's test (1982) and also a modified version of his test to see how the geometric approach of secondary school students (Grades 8-10) specialized in mathematics had changed. We observed two groups of students for several years. Our aim was to find a relation between the change of the mean of the van Hiele level of the students and the structure of the geometry syllabus. We also observed if there was a change in the geometric approach of the students during the summer holidays and if so, in what way it changed. -
Cooperative learning in teaching mathematics: the case of addition and subtraction of integers
117-136Views:27In the course of teaching and learning mathematics, many of the problems are caused by the operations with integers. My paper is a presentation of an experiment by which I tried to make the acquisition of these operations easier through the use of cooperative methods and representations. The experiment was conducted in The Lower-Secondary School of Paptamási from Romania, in the school year 2009-2010. I present the results of the experiment. -
The role of computer in the process of solving of mathematical problems (results of research)
67-80Views:30We would like to present results of an almost two years investigations about the role computer in the process of solving of mathematical problems. In these investigations took part 35 students of the secondary school (generalists) in the age 17–19 years. Each of these students solved following problem:
Find all values of the parameter m so that the function
f(x) = |mx + 1| − |2x − m| is:
a) bounded,
b) bounded only from the bottom,
c) bounded only from above,
first without a computer and next with a special computer program. We would like to show results of these researches. -
Nice tiling, nice geometry!?!
269-280Views:32The squared papers in our booklets, or the squared (maybe black and white) pavements in the streets arise an amusing problem: How to deform the side segments of the square pattern, so that the side lines further remain equal (congruent) to each other? More precisely, we require that each congruent transformation of the new pattern, mapping any deformed side segment onto another one, leaves the whole (infinitely extended) pattern invariant (unchanged).
It turns out that there are exactly 14 types of such edge-transitive (or so-called isotoxal) quadrangle tilings, sometimes with two different forms (e.g. black and white) of quadrangles (see Figure 2). Such a collection of tiling can be very nice, perhaps also useful for decorative pavements in streets, in flats, etc.
I shall sketch the solution of the problem that leads to fine (and important) mathematical concepts (as barycentric triangulation of a polygonal tiling, adjacency operations, adjacency matrix, symmetry group of a tiling, D-symbol, etc). All these can be discussed in an enjoyable way, e.g. in a special mathematical circle of a secondary school, or in more elementary form as visually attractive figures in a primary school as well.
My colleague, István Prok [11] developed an attractive computer program on the Euclidean plane crystallographic groups with a nice interactive play (for free download), see our Figures 3-5.
A complete classification of such Euclidean plane tilings (not only with quadrangles) can be interesting for university students as well, hopefully also for the Reader (Audience). This is why I shall give some references, where you find also other ones.
Further problems indicate the efficiency of this theory now. All these demonstrate the usual procedure of mathematics and the (teaching) methodology as well: We start with a concrete problem, then extend it further, step-by-step by creating new manipulations, concepts and methods. So we get a theory at certain abstraction level. Then newer problems arise, etc.
This paper is an extended version of the presentation and the conference paper [7]. The author thanks the Organizers, especially their head Professor Margita Pavlekovic for the invitation, support and for the kind atmosphere of the conference. -
Preliminary e ects of mathematics curriculum development for primary school student teachers in Sárospatak Comenius Campus
95-107Views:28Hungarian students' mathematics performance has been getting weaker in the past few years. A possible solution to stop this tendency is to develop curriculum. Therefore, Hungarian researchers have been refining a particular framework of curriculum development in primary school teacher training programmes. The national curriculum is designed on the assumption that learning can be broken into a sequence of levels and students can evenly succeed in gaining knowledge at successive levels. In this paper, we want to discuss how to reduce students' difficulties with different background to grow competence at successive levels. -
Teaching of old historical mathematics problems with ICT tools
13-24Views:15The aim of this study is to examine how teachers can use ICT (information and communications technology) tools and the method of blended learning to teach mathematical problem solving. The new Hungarian mathematics curriculum (NAT) emphasizes the role of history of science, therefore we chose a topic from the history of mathematics, from the geometry of triangles: Viviani's Theorem and its problem field. We carried out our teaching experiments at a secondary school with 14-year-old students. Students investigated open geometrical problems with the help of a dynamic geometric software (GeoGebra). Their research work was similar to the historical way. -
Guided Discovery in Hungarian Education Using Problem Threads: The Pósa Method in Secondary Mathematics Classrooms
51-67Views:108In Hungary, ‘guided discovery’ refers to instruction in which students learn mathematical concepts through task sequences that foster mathematical thinking. A prominent figure of guided discovery is Lajos Pósa, who developed his method to teach gifted students. Rather than teaching mathematics through thematic blocks, the Pósa Method employs webs of interconnected problem threads in which problems are built on each other, and different threads are presented simultaneously, so that students work on problems from multiple threads at the same time. It was found that this method has been successful as extracurricular training for gifted students since the 1980s; however since 2017, as part of an ongoing research, the method has been applied to mainstream curriculum in two public secondary school classrooms. The present paper examines the design and implementation processes of problem threads in this public secondary school context.
Subject Classification: 97D40
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Artworks as illustrations in Hungarian high school Mathematics textbooks
103-117Views:64Three different series of Hungarian Mathematics textbooks used in grade 9-12 education for the past 30 years have been analysed in this research. Our aim is to show and evaluate how the visual arts have been connected to mathematical ideas in these textbooks. We have applied the six dimensions of evaluation, which have recently been introduced in (Diego-Mantec on, Blanco, Búa Ares, & González Sequeiros, 2019) to categorise the illustrations of the three different series. We show examples for each dimension from the textbooks, and we find that even if the number of artistic illustrations in these coursebooks have significantly increased, in most cases these sporadic examples are not closely related to the mathematical context, mainly used for ornamental purposes to decorate the core text. Based on this classification we conclude that the number of artistic illustrations with underlying math concepts making students' participation more active could and should be significantly increased.
Subject Classification: 97U20
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Methodological questions of digital teaching material development made in the subject of mathematics
25-41Views:29In the methodology of mathematics teaching, the selection and the manner of using applicable digital teaching materials appeared as a new element. As the number of digital teaching materials applicable in education is constantly increasing, their purposeful use is rarely discussed. In what areas digital teaching materials can be used in mathematics? What are the problems for which they could provide a solution? Shall we use them besides traditional solutions, or instead?
The authors of this article have had the opportunity to participate in projects aiming to develop digital learning materials on various occasions. During the implementation of the projects, they needed to make methodological compromises at various points.
In our article, we are seeking a more emphatic use of methodology belonging to digital teaching materials, drawing on the experiences of three implemented projects. Our aim is to draw the attention to the anomalies we found in the implementation of the projects, which must be taken into consideration in new developments already at the planning stage. -
Experiences in the education of mathematics during the digital curriculum from the perspective of high school students
111-128Views:166Due to the COVID-19 epidemic, Hungarian schools had to switch to a digital curriculum for an extended period between 2019 and 2021. In this article, we report on the experiences regarding the education of mathematics during the digital curriculum in the light of the reinstated on-site education, all through the eyes of high school students. Distance education brought pedagogical renewal to the lives of many groups. Students were asked about the positives and negatives of this situation.
Subject Classification: 97C90
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Design guidelines for dynamic mathematics worksheets
311-323Views:15In a Math and Science Partnership project in Florida, middle school teachers are using the dynamic mathematics software GeoGebra to create interactive online worksheets for mathematics learning. Formative evaluation of these materials based on design principles of multimedia learning has lead to a list of specific design guidelines for such dynamic worksheets that we present in this article. These design guidelines can give advice both for the creation of new dynamic worksheets and the evaluation of existing material on the Internet. -
Report of meeting Researches in Didactics of Mathematics and Computer Sciences: January 25-27, 2013 Oradea, Romania
123-143Views:9The meeting Researches in Didactics of Mathematics and Computer Sciences was held in Oradea, Romania from the 25th to the 27th of January, 2013 at the Partium Christian University. It was organized by the PhD School of Mathematics and Computer Sciences of the University of Debrecen and the Partium Christian University in Oradea. The meeting was supported by the project: TAMOP-4.2.2/B/10/1-2010-0024.
The 61 participants – including 50 lecturers and 21 PhD students – came from 5 countries, 22 cities and represented 35 intstitutions of higher education. -
Teaching polygons in the secondary school: a four country comparative study
29-65Views:30This study presents the analysis of four sequences of videotaped lessons on polygons in lower secondary schools (grades 7 and 8) taught by four different teachers in four different countries (Belgium, Flanders, England, Hungary and Spain). Our study is a part of the METE project (Mathematics Educational Traditions in Europe). The aims and methodology of the project are described briefly in the introduction. In the next section of this paper we describe various perspectives on teaching and learning polygons which were derived from the literature, concerning the objectives, conceptual aspects and didactic tools of the topic. The next two sections introduce the main outcomes of our study, a quantitative analysis of the collected data and a qualitative description linked to the perspectives on teaching polygons. We conclude by discussing some principal ideas related to the theoretical and educational significance of this research work. -
Forming the concept of parameter with examples of problem solving
201-215Views:29Pupils are encountering difficulties with learning algebra. In order for them to understand algebraic concepts, particularly the concept of parameter it was decided by the teacher of mathematics and Information Technology to integrate the teaching of these two subjects. The aim of this study is to investigate whether, and to what degree, software can be useful in process of forming the concept of parameter. This longitudinal study was conducted in a junior high school (13-16 year old children) using different computer programs. -
Comparative geometry on plane and sphere: didactical impressions
81-101Views:2Description of experiences in teaching comparative geometry for prospective teachers of primary schools. We focus on examples that refer to changes in our students' thinking, in their mathematical knowledge and their learning and teaching attitudes. At the beginning, we expected from our students familiarity with the basics of the geographic coordinate system, such as North and South Poles, Equator, latitudes and longitudes. Spherical trigonometry was not dealt with in the whole project. -
Realizing the problem-solving phases of Pólya in classroom practice
219-232Views:119When teaching mathematical problem-solving is mentioned, the name of Pólya György inevitably comes to mind. Many problem-solving lessons are planned using Pólya's steps and helping questions, and teachers often rely on his heuristics even if their application happens unconsciously. In this article, we would like to examine how the two phases, Making a plan and Looking back, can be realized in a secondary school mathematics lesson. A case study was designed to observe and analyse a lesson delivered using cooperative work.
Subject Classification: 97B10, 97C70, 97D40, 97D50
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Group Work at High School According to the Method of Tamás Varga
167-176Views:74The aim of our research is to develop students’ logical thinking. For this reason, Hungarian mathematics teachers need to be encouraged to try new methods which induce greater student involvement. Research all over the world prove that self-instruction or self-verbalizing has high effect on the learning process. This was one of the key elements of Tamás Varga’s experiment in high school. In our classroom experiments we are using a special cooperative method from Kagan among 14-18 years old students, called Sage and Scribe structure. We are looking for the answers to the following question: Does this method make mathematics lessons more enjoyable and more comfortable for students? Furthermore, we assume this structure could open the gate toward other collaborative and cooperative teaching technics.
Subject Classification: 97D40
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Mathematical Doctoral School of the Mathematical Seminar of the University of Debrecen at the beginning of the 20th century (Debrecen, 1927-1940)
195-214Views:13In this article, we present the life and carrier of Professor Lajos Dávid, and those 16 mathematical dissertations, along with their authors, which were written under the supervision of Professor Dávid between 1927 and 1940. At the time mentioned, Lajos Dávid was the leader of the Mathematical Seminar of the University of Debrecen. The themes of the dissertations were connected with his scientific work, such as the history of mathematics (the two Bolyais), or his research work in mathematical analysis (arithmetic-geometric mean).